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Homework 3 Key

# Homework 3 Key - CHEMISTRY 201X Homework#3"Condensed Matter...

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CHEMISTRY 201X: Homework #3 Due : Thursday, September 20, 2007 “Condensed Matter” (1) (20 points) When fossil fuels undergo combustion, they produce the greenhouse gas CO 2 (g). Hydrogen is an attractive, alternative, “clean burning” fuel, because it produces just water vapor. This problem will examine some of the chemical issues to use hydrogen as a fuel for automobiles. (a) A standard sized fuel tank in an automobile holds ca. 50.0 L of octane (density = 0.698 g/mL at 300 K). When 1.00 mole of octane undergoes combustion, 5.074 × 10 3 kJ of energy are released, which is used to operate the car. When 1.00 mole of hydrogen burns, 2.418 × 10 2 kJ are released. How many moles of H 2 gas would be needed to provide the same amount of energy as a filled 50.0 L tank of octane? 50.0 L octane (C 8 H 18 ) = 3.49 × 10 4 g = 306 mol octane = 1.55 × 10 6 kJ released. Need 6.42 × 10 3 mol H 2 . (b) We could try to store hydrogen gas itself. Assuming ideal gas behavior, what volume (in L) would a tank need to be to store this amount of hydrogen gas at a pressure of 100.0 atm and 298.15 K? Now, treat hydrogen as a real gas using the van der Waals equation of state. What volume (in cm 3 ) would be needed? Explain your outcomes between the ideal and real gas models. Ideal Gas: V = nRT/p = (6.42 × 10 3 mol)(0.0821 L atm/mol K)(298.15 K) / (100.0 atm) = 1.57 × 10 3 L. Real Gas: (use van der Waals equation) [100.0 + 0.2444(6.42 × 10 3 /V) 2 ] [V (6.42 × 10 3 )(0.02661)] = 1.571 × 10 5 Solve by successive approximations starting with V

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Homework 3 Key - CHEMISTRY 201X Homework#3"Condensed Matter...

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